762 



We represent these five terms successively by A, B, C, D, E. 

 Sul)stitiiting equations (1) in 



- X r,. = \ V-ÏJ ^.jji.,-^—- \ r),. V-ci 2 y=<,3 ~ —^ 



ji-- 0.1-7 OXfi y,.irp d.Vy_ 0.r^3 



(d„^l, wlien ö = r; fr„:= 0, when (>^=i') we obtain 



, /•ö(7^/0 ea.,,(2)\/Ö7rp(i) Öy„v2) 





where t„<') and r„(-' represent tlie vabies of r„ in the case of only 

 the tirst or second centre. We put 



'0 f "2) 1 I 



— k:„ = — xr,./ — Jctj./ + p + q- 

 In calculating p and 7 we have considered, that y^i?^ and y(^"^J are 



zero, except when i? = r resp. ,J ^ «. Moreover as terms to be dif- 

 ferentiated with respect to .r^ give zero, the field being stationary, 

 we might everywhere replace yW and yf"^) by — 1. 

 When we now put 



(2) becomes 



^ A (^A+B^C + D + E) = x(£^ + rl!' ) + x(d!^ + r^!^) - p-q+xï„ . 

 As the field of each centre separately satisfies (2) we have 

 :S ^ = :« fïCi) + t(i) Vnd -S ^ = X Tï'S) 4. ((2) ) 



and so we obtain 



a/S/^ 0.«ï 



or, by further reduction of J, 



CT(o)Ay„=^— - + -S-— +p + 9-XÏ.. ... (3) 

 We now have to consider that in neglecting terms of the second 



